Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x+y &= -8 \\ 4x-y &= 6\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-y = -4x+6$ Divide both sides by $-1$ to isolate $y$ $y = {4x - 6}$ Substitute this expression for $y$ in the first equation. $-5x+({4x - 6}) = -8$ $-5x + 4x - 6 = -8$ Simplify by combining terms, then solve for $x$ $-1x - 6 = -8$ $-1x = -2$ $x = 2$ Substitute $2$ for $x$ back into the top equation. $-5( 2)+y = -8$ $-10+y = -8$ $y = 2$ $y = 2$ The solution is $\enspace x = 2, \enspace y = 2$.